New results on $\nu_{\mu}\to\nu_{\tau}$ appearance with the OPERA experiment in the CNGS beamarXiv: xxxx.xxxx

The analysis of the 2008-2009 inclusive sample (30% of the overall number of pot) was reported in ref2ndoscpaper. In that sample of 2738 fully analysed events one event was recognised as a $\nu_{\tau}$ candidate decaying to a single charged hadron (noted as $\tau\to 1h$)ref1sttau. More precisely the measurement of the final state topology and kinematics strongly favors this interpretation: $\tau^{-}\to\nu_{\tau}\rho^{-}$ with $\rho^{-}\to\pi^{-}\pi^{0}$ and $\pi^{0}\to\gamma\gamma$.

Since then the scanning strategy has been modified to accelerate the finding of a significant signal for $\nu_{\mu}\to\nu_{\tau}$ oscillation. Priority was given to the scanning of a pre-selected sample of bricks:

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  2008-2009 data: analysis of up to two bricks per event without event pre-selection.

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  2010 data: analysis of the HPBs, for all $0\mu$ events and for $1\mu$ events with a muon momentum $p_{\mu}<15$ GeV/$c$.

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  2011 data: analysis of the HPBs for all $0\mu$ events.

This pre-selection is temporary and the analysis of lower-priority bricks will occur in the near future.

$0\mu$ events form a preferred sample to search for $\tau$ decays since these essentially contain signals of the electron final state, with a branching ratio of $(17.85\pm 0.05)$%, and of the 1-prong, $(49.52\pm 0.07)$% and 3-prong, $(15.19\pm 0.08)$% hadronic channels.

In the $1\mu$-decay channel, with a branching ratio of $(17.36\pm 0.05)$%, most events occur at low muon momentum. This is due to the fact that the atmospheric-scale oscillation, at this baseline, mainly affects the low-energy region. Moreover, a large fraction of the $\tau$ momentum is transferred to the two final-state neutrinos. This is illustrated in the left plot of Fig. 2 which also shows the distributions of the reconstructed signed muon-momentum ($q\times p_{\mu}$) for $1\mu$-events for data and Monte Carlo (MC). The shape of the data is well described by MC, indicating that the pre-selection of events is well understood. The momentum cut at 15 GeV/$c$ (dashed lines) results in a loss in the sample of muonic $\tau$ decays of only 4%. Instead, this cut reduces by 33% the amount of $\nu_{\mu}^{CC}$ events to be analysed and, more important, by 28% the size of the charm sample. The momentum cut at 15 GeV/$c$ is also applied to the 2008 and 2009 samples at a later step of the analysis chain in the kinematical selection proposal (see, Sect. 3.5).

The right plot in Fig. 2 shows the distributions of the brick probability for $0\mu$ and $1\mu$ events of the 2010 and 2011 samples, separately for the first two bricks in the probability ranking. Again, the shape of the brick probability is well described by MC. Details on the MC simulation will be given in Sect. 4.

The number of events selected at the level of electronic detectors ($N_{ED}$) is 11149 (listed for each year in the first row of Tab. 2). Part of this sample is discarded by the brick finding algorithm based on the topology of the measured hits in the TT. The rejected sample is mainly accounted for by punch-through of external interactions. The numbers of events with a good brick prediction, which are sent to the scanning laboratories ($N_{pred}$, 9267 in total), are given in the 2^nd row in Tab. 2.

Selected bricks are routinely extracted by a robotic Brick Manipulator System (BMS) capable of keeping up with the average weekly rate of neutrino interactions and thus allowing for the emulsion-based analysis to potentially proceed in parallel to the neutrino interactions data taking. Removed bricks with a negative CS result are re-inserted in the target after replacement of the CS while dismantled bricks are not replaced. Empty spaces are filled by a rearrangement of bricks. This approach aims at keeping the target homogeneous and minimise the occurrence of events with irregularities in the energy flow containment. The position of each brick is registered in a dynamic database to enable the event location.

The average number of bricks in the detector during each run is given in the last column of Tab. 1. The time evolution of the target mass is shown in more detail in Fig. 3 (blue curve) together with the integrated number of pot (corrected for the inefficiency of the DAQ system, red curve). The loss in target mass at the end of the running amounts to 8.5% of its maximum value.

The pre-selected events ($N_{ED}$) represent a fraction of 78% and 33% of the 2010 and 2011 contained-event samples, respectively.

After the extraction of the selected brick from the detector, the scanning of the CS doublets is performed in order to validate or disprove the brick-finding result. The pattern of tracks reconstructed in the CS doublets can confirm the prediction of the electronic detector, or act as veto and thus trigger the extraction of neighbouring bricks.

CS doublets are inspected by automatic optical scanning microscopes ref14_d; uts_a; uts_b; uts_c; uts_d; ess_a; ess_b; ess_c; ess_d; ess_e in two specialised scanning stations at the LNGS laboratory and at Nagoya University. A rectangular shape is defined centered on the prediction of the electronic detectors with a resulting average scanning area of 20 cm² for $1\mu$ events and 35 cm² for $0\mu$ events, the pointing accuracy here being poorer due to the absence of a muon track.

The tracking efficiency of the CS doublets has been measured in neutrino data and test beam exposures CSpaper; CSpaperJP. A charged particle crossing the CS will produce 4 track segments called micro-tracks. The micro-track detection efficiency for minimum ionising tracks is 95% CSpaperJP with the automatic scanning system. The distributions of the residuals in position and angle between the ED and CS tracks have a standard deviation of about 8 mm and 15 mrad respectively.

The analysis and scanning strategy have been improved during the years. In the analysis of the 2008 and 2009 runs, a brick was sent to development as soon as at least one CS track had a possible match with some ED hits. Subsequently the strategy (“CS trigger”) has been refined for the 2010 and 2011 runs by requiring the presence of at least:

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  for $1\mu$ events, a CS track compatible with the ED muon track within 60 mrad

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  for 0$\mu$ events, a CS track matching an isolated ED track

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  2 or more CS tracks possibly converging towards a common origin in the brick.

If none of these conditions are fulfilled, the brick is put back in the target with a new CS doublet and the next brick in the probability map is extracted (in case of multi-brick analysis). This method allows saving scanning and analysis time and minimising the target mass loss. In case of a positive outcome, the brick is exposed to cosmic rays in a dedicated pit in the surface LNGS laboratory for 14 hours for high-precision film-to-film alignment, later to be dismantled in the dark room where the emulsion films are developed. The films are finally dispatched to the scanning laboratories of the Collaboration for the “vertex location” and “decay search” analysis.

CS tracks are projected to the most downstream emulsion film in the brick (through a distance of about 4.5 mm mainly filled with the plastic and Aluminium film of the CS and brick boxes) where they are searched for. The residuals in position are at the level of 50-60 $\mu$m such that the tracks are typically found within the predicted microscope view (400 $\times$ 300 $\mu$m). They are then followed upstream film by film (“scan-back”scanback_a; scanback_b) adjusting the predictions in angle and position at each step to cope with multiple Coulomb scattering (MCS) in the lead plates and measurement errors effects.

The scan-back procedure is stopped when no track candidate is found in three consecutive films; the lead plate just upstream of the last detected segment is defined as the candidate vertex plate. At this stage a volume is defined with a transverse area of 1 cm² for 5 films upstream and 10 films downstream of the stopping point (or less if the stopping point lies too upstream or downstream in the brick) and tracks within an angular acceptance $\tan\theta<0.6$ ($\theta$ being the angle of the track with the $z$ axis, Fig. 1) are searched for in this volume (general scan).

The scan-back procedure is modified for events in which the CS-trigger is produced only by a shower-like topology (mainly due to $\gamma$ conversions from $\pi^{0}$ decays). In such cases an area of 1 cm² centered on the shower axis is analysed for 20 films (corresponding to about 3.5 $X_{0}$) starting from the last plate.

All track segments collected in the scanned volumes are analysed by offline algorithms which perform precise alignment, tracking and vertexing. The alignment of the films (with an accuracy of a few $\mu$m) is assured by the cosmic ray tracks (Sect. 3.2).

In some cases the scan-back track is not associated to any other track inside the volume due to a low-multiplicity event or because of the angular acceptance limitation or tracking inefficiencies. In this condition the vertex is consider as detected. A further signature of the neutrino interaction can then be obtained from the analysis of nuclear fragments which might be visible in the forward and/or backward hemisphere especially if the interaction happened close to the emulsion layers. Dedicated image analysis tools have been developed largeangle_a; largeangle_b to detect highly ionising large-angle tracks in the proximity of the stopping point.

Interactions are tagged as “dead material” when the extrapolated vertex does not lie in the lead plates or in the films (i.e. it is in the scintillator strips, in the brick supporting structure) and no event-related tracks are found in the upstream-brick CS-doublet.

For the 2008-2011 analysed sample, the events located in the brick lead plates ($N_{brick}$) amount to 4135 (Tab. 2).

The decay search (DS) procedure is aimed at detecting the decay topologies of $\tau$ leptons produced in $\nu_{\tau}^{CC}$ interactions once a vertex has been identified in the volume scan data. The decay is defined as “short” if it happens in the same lead plate where the neutrino interaction occurred or in the first downstream emulsion layer and as “long” if it happens further downstream such that at least one complete micro-track is produced by the $\tau$-lepton. About 46% of the $\tau$ decays are expected to be short (43% in the first lead plate and 3% in the first emulsion layer) while the remaining 54% are long decays happening in the first plastic base (11%), in the second emulsion layer (2%), in the second lead plate (25%) or further downstream (16%).

Candidate daughter tracks from short-lived particles decays are selected by requiring their impact parameter ($IP$) with respect to the reconstructed neutrino interaction vertex to be larger than 10 $\mu$m if the depth in lead ($\lambda$) is lower than 500 $\mu$m or by loosening this requirement to $IP>(5+0.01\times\lambda)$ $\mu$m for deeper vertices. The next requirement is that the momentum of the candidate daughter track measured from its MCS ($p_{mcs}$) MCSpaper is larger than 1 GeV/$c$. If the number of planes in the scanned volume is not sufficient to estimate $p_{mcs}$ the angular spread $S_{\theta}$ of the available segments is evaluated (see refDS for a detailed definition). If $S_{\theta}>15$ mrad in both views, the track is discarded, otherwise the MCS measurement is extended to more plates.

A search is then performed for additional tracks (called extra-tracks) which are not directly connected to the primary vertex: they must be detected in at least 3 films and the distance along the $z$-axis between the most upstream segment and the neutrino vertex ($\Delta z=z_{up}-z_{vtx}$) is required to be positive and less than 3.6 mm. In addition we require $IP<$ 300 $\mu$m if $\Delta z<$ 1 mm and $IP<$ 500 $\mu$m for $\Delta z>$ 1 mm.

In order to deal with topologies in which the first-reconstructed vertex is the decay vertex and thus downstream of the primary neutrino vertex (e.g. in a $\tau\to 3h$ decay) the search for extra tracks is also extended upstream, requiring $\Delta z>-2$ mm and $IP<$ 500 $\mu$m. For the events located on the basis of a single track (which could be due to a higher-multiplicity decay with tracks outside of the scanning angular acceptance), extra-tracks are searched for within a $\Delta z$ of $\pm$ 3 mm and $IP<500$ $\mu$m. In this case the $z$ position of the vertex is assumed to be at the center of the lead plate.

A search for charged short-lived parents is then applied to both upstream and downstream extra-tracks by looking for tracks or single segments with $IP<10$ $\mu$m and a distance of closest approach $d_{ca}<$ 20 $\mu$m with respect to the possible daughter tracks.

Finally the presence of a significant kink (larger than 20 mrad) is checked on the muon track for $1\mu$ events and on all tracks for $0\mu$ events. The four most upstream segments of the track are used to evaluate the ratio ($R$) between the maximum angular difference between pairs of segments and the overall angular spread refDS. If $R>5$ then a “kink trigger” is issued and further analysis is performed.

All these operations are supplemented by manual eye-inspection at the microscope in order to improve the information provided by automatic scanning in terms of angular resolution (the automatic system accuracy can sometimes be spoiled by the association of uncorrelated background grains) and efficiency (by recovering the information for inefficient planes). Eye-inspection is also employed to improve the purity by discarding fake tracks (most important for large angles and high-fog²² 2 AgBr crystals can be activated in the emulsion due to thermal or mechanical excitations resulting in the presence of randomly distributed grains which are referred to as “fog”. films), and furthermore allows excluding passing–through cosmic ray tracks which can mimic extra-tracks due to inefficiencies of the automatic scanning in the five upstream films.

The number of events with a completed decay-search ($N_{DS}$) for the present analysis amounts to 3969 (Tab. 2). This number differs from $N_{brick}$ by about 4% due to the events which fall at the edges of the brick (either in the longitudinal plane or in the transverse direction).

Several kinematic quantities of the neutrino interaction are accessible at brick-level via momentum reconstruction using MCS. The energy of electrons and photons is also measured by employing calorimetric techniques EMrec; nuepaper. Kinematic criteria can be defined to improve the signal-to-background ratio. To improve the acceptance for electromagnetic showers and reduce the error on the track momentum measurement the standard volume considered for the location (Sect. 3.3) is enlarged and tracks are followed downstream, eventually in other bricks (Sect. 3.6).

After denoting the charged tracks emerging from the neutrino interaction vertex or the decay vertex as “primaries” and “daughters” respectively, and the short-lived primary track as “parent”, we define the following relevant variables:

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  $z_{dec}$: the $z$-coordinate of the decay vertex with respect to the downstream face of the lead plate containing the primary vertex ($z_{dec}<44~\mu$m for short decays).

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  $p_{T}^{2ry}$: the transverse momentum of the daughter with respect to the parent direction, for 1-prong decays.

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  $p_{T}^{miss}$: the magnitude of the vectorial sum of the transverse momenta of primaries (except the parent) and daughters with respect to the neutrino beam direction.

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  $p^{2ry}$: the scalar sum of the momenta of the daughters.

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  $\theta_{kink}$: the average 3D angle between the parent and its daughters (kink angle).

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  $m$: the invariant mass of the daughters (calculated attributing the $\pi$ mass).

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  $m_{min}$: the minimal invariant mass ref:mininvmass.

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  $\phi_{lH}$: the angle between the parent and the vectorial sum of the other primaries calculated in the plane perpendicular to the CNGS axis.

In the calculation of $\phi_{lH}$, if the primary multiplicity (including the $\tau$ track candidate) is larger than two, the primaries are defined after removal of the track with the largest difference in $\phi$ with respect to the $\tau$ candidate (TLD) unless it is identified as a hadron with high probability by the track follow-down procedure (Sect. 3.6). This is intended to remove events where the TLD is actually a genuine muon which has not been identified as such by the electronic detectors (for these events, if the TLD would not be excluded the angle would be large and thus the kinematic cut on this variable would not be effective).

The applied selections are summarised for each channel in Tab. 3. The choice of cut parameters has been studied and defined in proposal for the 1$h$, electron and muon channels and in tesiAntonia for the 3$h$ channel.

The track kinematics of interesting events fulfilling the selection are further studied in neighbouring bricks. Primary tracks are followed (with an angular acceptance extending up to $\tan\theta=1$) until either a stopping point, an interaction or a muon decay topology is found (track follow-down, TFD). Thus, by the study of momentum-range correlations, track length, energy loss in proximity of the stopping point, and (if possible) the tagging of interactions or muon decays, a muon/hadron separation exceeding the limitations of the electronic detector reconstruction is obtained.

This procedure results in a significant reduction of the background in all channels from $\nu_{\mu}^{CC}$ charm production where the primary $\mu$ is not identified in the ED. The TFD technique also provides an important reduction of the background in the $\tau\to\mu$ channel from $\nu_{\mu}^{CC}$ events in which the primary $\mu$ is wrongly associated to a secondary vertex with a kink topology from a hadronic re-interaction. This also holds for $\nu_{\mu}^{NC}$ events with a fake muon. The improved muon/hadron separation provided by TFD is also effective in reducing the background in the hadronic channels due to hadron re-interactions in $\nu_{\mu}^{CC}$ events where the electronic detectors alone do not allow the primary $\mu$ to be identified unambiguously.

Momentum-range correlations are characterised by a discriminating variable defined as: $D_{TFD}=\frac{L}{R(p)}\frac{\rho}{\langle\rho\rangle}$ where $L$ is the track length, $R(p)$ is the range in lead of a muon with momentum $p$, $\langle\rho\rangle$ is the average density along the path and $\rho$ is the lead density. The MC distributions of $D_{TFD}$ for hadrons and muons are reported in Fig. 6. If $D_{TFD}>0.8$ the track is classified as a muon. Among all the criteria used to separate muons from hadrons, momentum-range correlations and energy loss close to the stopping point, are those having a lower purity in the muon-tagging. For this reason, TLD tracks which are classified by the TFD as hadrons only by one of the above criteria are not included in the calculation of $\phi_{lH}$.

The neutrino fluxes used in the calculation of the expected signal rates are based on a FLUKA fluka simulation of the CNGS beam-line (2005 revision CNGSflux). The neutrino interactions in the detector are generated using the NEGN generator after a tuning of the parameters based on the high-statistics data sample of the NOMAD experiment NOMADtuning . The energy-dependence of the $\nu_{\tau}$ cross section that has been used is the default implementantion contained in the GENIE v2.6 simulation program GENIEcit. The $\nu_{\mu}\to\nu_{\tau}$ oscillation probability was evaluated using $\Delta m^{2}_{23}=2.32\times 10^{-3}$ eV² PDGdm2 and $\sin^{2}2\theta_{23}=1$. With these ingredients, the expected rate of $\nu_{\tau}^{CC}$ on lead at true level is equal to $3.32$ events/(10¹⁹ pot kt). Taking into account the time evolution of the pot delivery rate and the effective mass of the detector throughout the running period (Fig. 3) a total number of 66.4 $\nu_{\tau}$ CC interactions in lead are expected (with the non-DIS component being about one third GENIEcit of the total).

The expected rate of $\nu_{\tau}^{CC}$ events in the $0\mu$ sample can be expressed in terms of the measured event rate in the same category ($n^{0\mu}$ from both $\nu_{\mu}^{CC}$ and $\nu_{\mu}^{NC}$) as:

denoting with $\langle\epsilon^{r}(k)\rangle$ the efficiency for reconstructing the process $k$ ($\nu_{\mu}^{CC}$, $\nu_{\mu}^{NC}$) in the reconstructed category $r$ ($0\mu$, $1\mu$) after convolution with the CNGS flux $\phi$; $N(\nu_{\mu}^{CC})$ being the $\nu_{\mu}^{CC}$ interactions at true level and $\alpha=\sigma(\nu_{\mu}^{NC})/\sigma(\nu_{\mu}^{CC})~\otimes~\phi$. In the present analysis the actual number of $n^{0\mu}$ is taken from the data while other quantities are MC driven. The expected numbers obtained with the above-mentioned procedure are insensitive to systematic effects on the efficiencies up to the location level being common to $\nu_{\tau}$ and $\nu_{\mu}$ events. The same approach is followed in the prediction of the $\nu_{\tau}$ component in the $1\mu$ sample. In this particular case, in addition to the standard $1\mu$ classification (Sect. 3), the presence of a muon tagged 3D track is also required due to the need of matching this ED track to the ECC secondary $\mu$ candidate track for the sake of background reduction.

Finally it must be noted that in the present approach the signal efficiency is not taking into account possible migrations between different channels and could therefore be slightly underestimated.

Three sources of backgrounds are giving significant contributions to the final sample: charmed particles decays, hadronic interactions and large-angle muon scattering (LAS). The last one only affects the $\tau\to\mu$ channel while the other classes differently affect all decay channels. These backgrounds have been discussed extensively in proposal. The basic ingredients for the more recent evaluation of these components will be discussed in the following.

This neutrino interaction occurred on 23 April 2011 at 7.15 UTC time. The pattern of hit scintillator strips in the TT is shown in Fig. 8. The event, of which the estimated hadronic energy is ($22.0\pm 6.2$) GeV, is classified as $0\mu$ and the bulk of the activity in the electronic detector is contained within about 6 to 8 brick walls (more than 60 $X_{0}$ and about 2.5 pion interaction lengths). The interaction took place in the target of the upstream Super Module and lies well within the brick-filled target region. The neutrino vertex brick (having a probability of 63%) was located in the longitudinal direction ($z$), in the second most upstream brick layer (called $W_{0}$), in the horizontal direction ($x$), in the 3^rd brick layer from the closest side (left side looking towards the CNGS) and, in the vertical direction ($y$), in the 19^th brick layer from the bottom. In Fig. 8 the position of the brick containing the interaction is highlighted. A linear extrapolation of the vertex tracks found in the emulsions (described in the following) is also shown to illustrate the matching with hits in the scintillators. The event emulsion data has been independently measured with the European and Japanese scanning systems with consistent results. The average values are considered in the following.

The interaction is well inside the brick in the longitudinal coordinate lying slightly upstream of the center of the brick (22^nd lead plate in increasing $z$ order) while in the transverse plane it lies at 6.8 mm and 41.4 mm from the closest sides in $x$ and $y$.

The topology of the primary vertex ($V_{0}$ in Fig. 9) consists of two tracks, the $\tau$ lepton candidate and another track (called $p_{0}$). The distance of closest approach of the $p_{0}$ and $\tau$ tracks equals to 0.2 $\mu$m and the vertex lies close to the downstream emulsion film, at a depth in lead of only 120 $\mu$m. A forward-going nuclear fragment associated to the primary vertex has also been detected at a large angle with slopes of: $(1.15,-0.28)$⁵⁵ 5 Slopes are given as tangents of the projected angles after correction for the 58 mrad vertical tilt of the beam. .

The flight length of the $\tau$ lepton candidate is (1466 $\pm$ 10) $\mu$m and its decay occurs in the plastic base allowing excluding with a high efficiency (above 99.8% at 90% C.L. up to $\tan\theta=3$, largeangle_a) the emission of highly ionising nuclear fragments. The secondary vertex ($V_{1}$,  Fig. 9) consists of three tracks (called $d_{1}$, $d_{2}$, $d_{3}$). A display of the reconstructed grains in the emulsion layers is presented in Fig. 10. The impact parameters of the decay products with respect to the reconstructed secondary vertex are 1.3, 1.2 and 0.3 $\mu$m for $d_{1}$, $d_{2}$ and $d_{3}$ respectively. After eye-inspection the background from instrumental fake tracks or tracks due to Compton electrons is negligible.

In the beam transverse plane the $\tau$ and the $p_{0}$ tracks form an angle $\Delta\phi_{\tau H}=(167.8\pm 1.1)^{\circ}$ (Fig. 11).

In order to strongly constrain the hypothesis that the secondary vertex could be a hadronic interaction, a search for nuclear fragments has been performed both upstream and downstream of the vertex with an automatic scanning up to $\tan\theta=3.5$ as well as by visual inspection. No such fragment was found.

A search for $\gamma$ conversions has been performed up to $\tan\theta=1$ for the 35 films (about 6 $X_{0}$) downstream of the vertex yielding no candidates.

The analysis of each track to determine its nature and momentum is described below:

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  track $p_{0}$ has a measured momentum $p_{p_{0}}=(2.8^{+0.7}_{-0.7})$ GeV/$c$. This track points towards the centre of the detector in the top-view such that its signature as a hadron is already well constrained using the target tracker information only. Nevertheless the track has been followed in the downstream wall ($W_{1}$) where it is found to exit the brick to the side. Compatible tracks have neither been found in the adjacent brick in $W_{1}$ nor in downstream bricks (and CS doublets) up to $W_{3}$. Gamma rays from a possible hadronic interaction were also searched for in two bricks in $W_{2}$, however, no $\gamma$ was found. This track is then assumed to interact in the dead material in-between two bricks. A muon with a momentum of the magnitude measured by MCS would be expected to travel from 26 to 44 brick layers before stopping. This makes the muon hypothesis very unlikely: $D_{TFD}$ is 0.05 for this track. Its projected slopes are $(0.155,-0.365)$, well inside the angular acceptance of the scanning. Even considering the possibility of having missed a muon track crossing the downstream emulsion detectors, the pattern in the scintillators does not allow the existence of such a track for more than about 7-8 brick walls.

• •

  track $d_{1}$ has slopes of (-0.056, 0.101) and a measured momentum $p_{d_{1}}=(6.6^{+2.0}_{-1.4})$ GeV/$c$. A hadronic interaction is detected in the emulsions of the brick in wall $W_{4}$ (see Fig. 8) producing two charged tracks with slopes of (0.234, 0.489) and (0.034, -0.305). The signature of the interaction is also indicated by the target tracker scintillators.

• •

  track $d_{2}$ has a slope of (-0.041, 0.260) and a measured momentum $p_{d_{2}}~=~(1.3^{+0.2}_{-0.2})$ GeV/$c$. It has not been found in $W_{2}$ or in the following walls corresponding to a range-momentum correlation parameter $D_{TFD}=0.25$.

• •

  track $d_{3}$ has a slope of (-0.134, 0.220) and a measured momentum $p_{d_{3}}~=~(2.0^{+0.9}_{-0.6})$ GeV/$c$. This track interacts in the brick containing the neutrino vertex, after 11 lead plates i.e. about 1.3 cm downstream ($V_{2}$ in Fig. 9). The interaction occurs inside the emulsion resulting in a very clear signature. The final state is composed of two charged tracks ($d_{3-1}$ and $d_{3-2}$) and four back-scattered nuclear fragments.

The scalar sum of the momenta of all the measured charged particles in the event is 12.7${}^{+2.3}_{-1.7}$ GeV/$c$.

From the arguments developed in ref1sttau; ref2ndoscpaper and in Sect. 5.1, it is concluded that the two events are candidates of $\tau$ decays into the 1-charged hadron ($1h$) and 3-charged hadrons ($3h$) channels, respectively. Table 5 summarises the values taken by the kinematic variables for the two candidates together with the cuts applied in the analysis.

The distributions of $\phi_{lH}$, for the expected signal and background components in the analysed sample are presented in Fig. 12 for the 1$h$ and 3$h$ channels separately. The measured values in the data are indicated by vertical lines.